Asymmetry correction in read signal

ABSTRACT

Systems and techniques associated with signal processing are described. A described technique includes generating asymmetry vectors that model asymmetry in a received analog signal, including an effect of asymmetry spreading in a read channel and selecting at least two different indicators of asymmetry based on the asymmetry vectors. The technique can include using the selected indicators of asymmetry to compensate for one or more asymmetries associated with the analog signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims the benefit of priorityunder 35 USC 120 of U.S. application Ser. No. 12/405,161, filed Mar. 16,2009 and entitled “ASYMMETRY CORRECTION IN READ SIGNAL” (issued as U.S.Pat. No. 7,817,368 which is a divisional of and claims the benefit ofpriority under 35 USC 120 of U.S. application Ser. No. 11/092,095, filedMar. 28, 2005 and entitled “ASYMMETRY CORRECTION IN READ SIGNAL” (issuedas U.S. Pat. No. 7,511,910), which is a continuation-in-part applicationof and claims the benefit of priority to U.S. application Ser. No.10/976,110, filed Oct. 27, 2004, and entitled “ASYMMETRY CORRECTION INREAD SIGNAL” (issued as U.S. Pat. No. 7,298,570), and which claims thebenefit of the priority of U.S. Provisional Application Ser. No.60/622,428, filed Oct. 27, 2004 and entitled “A NEW ADAPTATION SCHEMEFOR ASYMMETRY CORRECTION FOR MAGNETIC RECORDING CHANNELS.” Thedisclosures of the prior applications are considered part of (and areincorporated by reference in) the disclosure of this application.

TECHNICAL FIELD

The present disclosure describes systems and techniques relating tosignal processing, for example, interpreting readback signals obtainedfrom a magnetic storage medium.

BACKGROUND

Signal processing circuits are frequently used to read storage media andinterpret obtained analog signals as discrete values stored on themedia. For magnetic storage media, a transducer head may fly on acushion of air over a magnetic disk surface. The transducer convertsmagnetic field variations into an analog electrical signal. The analogsignal is amplified, converted to a digital signal and interpreted(e.g., using maximum likelihood techniques, such as using a Viterbidetector). Tracking of stored data during a read operation is frequentlyperformed using feedback or decision aided gain and timing control.Additionally, perpendicular magnetic recording techniques can be used toincrease the amount of data stored on a magnetic medium, andpost-processing techniques can be used to detect and correct errors madeby the main detector in magnetic recording systems.

The head-media combination in typical magnetic recording systems hasassociated transfer characteristics that include an asymmetrical signalamplitude response, where an input signal having equivalent amplitudeson the positive and negative sides of the waveform results in an outputsignal having different amplitudes on the positive and negative sides ofthe waveform. Such amplitude asymmetry has been compensated for byadding to a readback signal an asymmetry adjustment signal, which is thereadback signal squared and then scaled by a controlled asymmetryfactor. The controlled asymmetry factor has previously been based on acomparison of the positive peak value with the negative peak value inthe readback signal, which thus minimizes amplitude error at the peakvalues.

SUMMARY

The present disclosure includes systems and techniques relating tointerpreting signals on a channel having an asymmetrical signalamplitude response. According to an aspect of the described systems andtechniques, a signal processor, such as a read channel transceiverdevice usable in a magnetic recording system, includes an asymmetrycorrection circuit configured to receive an analog signal and tocompensate for asymmetry in the received analog signal, a signalequalizer configured to receive an input signal responsive to an outputof the asymmetry correction circuit and to generate an equalized signal,a discrete time sequence detector operable to examine the equalizedsignal, and a control circuit that provides a coefficient adjustment tothe asymmetry correction circuit to affect the asymmetry compensationbased on an estimate of nonlinearity derived from the equalized signaland multiple output values of the discrete time sequence detector, themultiple output values being values corresponding to at least twodifferent discrete times.

The coefficient adjustment can include one or more values received bythe asymmetry correction circuit to control the asymmetry compensation.These values can be coefficient values or coefficient adjustment values(e.g., a coefficient adjustment can be a coefficient value q_(k+1) or acoefficient adjustment value μ·β, when the coefficient value isgenerated according to q_(k+1)=q_(k)+μ·β, as described further below).The asymmetry correction circuit, the signal equalizer, the discretetime sequence detector and the control circuit can form at least aportion of a read channel in a storage access device, and the analogsignal can be a readback signal obtained from a storage medium.

The multiple output values of the discrete time sequence detector caninclude values corresponding to discrete times that fall both before andafter a current time. The control circuit can be configured to derivethe estimate of nonlinearity from the equalized signal and multipleasymmetry indicators, where an asymmetry indicator includes a product oftwo reconstructed, ideal channel output values.

The asymmetry indicators can be selected based on a comparison ofmultiple, converged, asymmetry matrices generated for different targetsfor modeling signal nonlinearity caused by magnetic recording channelasymmetry. The different targets can include a DC target and a DC-freetarget. The control circuit can include a programming interfaceconfigured to enable program control over relative contributions of themultiple asymmetry indicators.

The asymmetry indicators can include a common-time indicator and aseparated-time indicator, the common-time indicator including a squareof a reconstructed, ideal channel output value, and the separated-timeindicator including a product of two reconstructed, ideal channel outputvalues corresponding to different discrete times. The control circuitcan include a programming interface configured to enable separateprogram control over relative contributions of the common-time indicatorand the separated-time indicator.

The coefficient adjustment can include one or more values received bythe asymmetry correction circuit to control the asymmetry compensation,the one or more values being generated at least in part according to anequation, q_(k+1)=q_(k)+μ₁β−μ₂χ, where q_(k) is an asymmetry correctioncoefficient at time k, μ₁ and μ₂ are programmable step sizes,β_(k+1)=β_(k)+μ_(b)·(y_(k) ^(r)−y_(k) ^(a))·y_(k) ^(d)·(y_(k+1)^(d)−y_(k−1) ^(d)), χ_(k+1)=χ_(k)+μ_(c)·(y_(k) ^(r)−y_(k) ^(a))·y_(k)^(d)·y_(k) ^(d), μ_(b) and μ_(c) are step sizes, y^(r) corresponds tothe equalized signal, y^(d) corresponds to an estimated ideal channeloutput derived from the output of the discrete time sequence detector,and y^(a) corresponds to an estimated real equalized channel output withasymmetry taken into account.

According to another aspect of the described systems and techniques, asystem includes a storage medium; a head assembly operable to obtain ananalog signal from the storage medium; an asymmetry correction circuitconfigured to receive the analog signal and to compensate for asymmetryin the received analog signal; a signal equalizer configured to receivean input signal responsive to an output of the asymmetry correctioncircuit and to generate an equalized signal; a discrete time sequencedetector operable to examine the equalized signal; and a control circuitoperable to provide a coefficient adjustment to the asymmetry correctioncircuit to affect the asymmetry compensation based on an estimate ofnonlinearity derived from the equalized signal and multiple outputvalues of the discrete time sequence detector, the multiple outputvalues being values corresponding to at least two different discretetimes.

According to yet another aspect of the described systems and techniques,a method includes compensating for asymmetry in an analog signal basedon at least one coefficient adjustment; equalizing a digital signalobtained by sampling the analog signal; detecting a data sequence in thedigital signal; reconstructing an ideal target channel output from thedetected data sequence; and modifying the at least one coefficientadjustment to affect the asymmetry compensation based on an estimate ofnonlinearity derived from the digital equalized signal and multipleoutput values of the reconstructed ideal target channel output, themultiple output values being values corresponding to at least twodifferent discrete times. The method can further include deriving theestimate of nonlinearity from the digital equalized signal and multipleasymmetry indicators selected based on a comparison of multiple,converged, asymmetry matrices generated for different targets formodeling signal nonlinearity caused by magnetic recording channelasymmetry, an asymmetry indicator comprising a product of tworeconstructed, ideal channel output values. Additionally, the method canfurther include controlling relative contributions of the multipleasymmetry indicators based on programmed input, wherein the asymmetryindicators include a common-time indicator and a separated-timeindicator.

The described systems and techniques can be implemented in electroniccircuitry, computer hardware, firmware, software, or in combinations ofthem, such as the structural means disclosed in this specification andstructural equivalents thereof, including a software program operable tocause one or more machines to perform the operations described.

The described systems and techniques can result in improved asymmetrycorrection in a read channel of a storage device, allowing a largerportion of the dynamic range of the head-media combination to be used.Nonlinearity observed over multiple discrete time units on the digitalside of a read channel can be used to provide a feedback signal thatcontrols the asymmetry correction applied on the analog side of the readchannel. The total output signal can be considered in optimizing one ormore coefficients applied in an asymmetry correction circuit.

The systems and techniques described can employ a straight forwardequation to calculate an error term for the adaptation of an asymmetrycorrection coefficient, and can be applied to many different targetchannels (e.g., a perpendicular magnetic recording channel or alongitudinal magnetic recording). Control of the asymmetry correctioncan be made programmable, allowing extensive flexibility in adjustingthe asymmetry correction employed in a channel in light of a specificapplication for the channel. For example, a read channel transceiverdevice can be designed for use with both direct current (DC) targets andDC-free targets, where the asymmetry correction can be programmed toprovide optimal results for a given target. Thus, the asymmetrycorrection can be tailored to a particular target channel of interest.

Details of one or more implementations are set forth in the accompanyingdrawings and the description below. Other features, objects andadvantages may be apparent from the description and drawings, and fromthe claims.

DRAWING DESCRIPTIONS

FIG. 1 is a block diagram showing a read channel in a storage systemthat performs amplitude asymmetry correction.

FIG. 2 is a block diagram illustrating the introduction of nonlinearityin the readback signal and the subsequent compensation for thisnonlinearity.

FIG. 3 is a graph illustrating an example of error over time during asimulation of a matrix approach to modeling asymmetry in a channel.

FIG. 4 is a flowchart illustrating a process of selecting signalindicators of asymmetry for use in asymmetry correction.

FIG. 5 is a block diagram illustrating an example asymmetry correctioncircuit (ASC).

FIG. 6 is a block diagram showing a magnetic-media disk drive thatemploys amplitude asymmetry correction as described.

FIG. 7 is a block diagram showing perpendicular magnetic recording ascan be used in the magnetic-media disk drive of FIG. 6.

FIG. 8 is a flowchart illustrating a process of asymmetry correction ascan be performed in a storage system.

DETAILED DESCRIPTION

FIG. 1 is a block diagram showing a read channel in a storage systemthat performs amplitude asymmetry correction. The storage systemincludes a storage medium 100 and read head 102. The storage medium canbe read-only or read/write media and can be magnetic-based,optical-based, semiconductor-based media, or a combination of these.Examples of the storage medium include hard disk platters in a hard diskdrive, a floppy disk, a tape, and an optical disk (e.g., laser disk,compact disk, digital versatile disk). The storage medium is depicted inFIG. 1 as a disk for illustration only; the systems and techniquesdescribed herein can be used with other storage media types or innon-storage applications (e.g., communications equipment).

The read head 102 can be part of a read-write head assembly that readsthe storage media 100 under the control of a servo or actuator. Ananalog readback signal is generated and can be sent to a pre-amplifier105. The system can include an analog front end (AFE) 110, which canprovide filtering and gain control. The AFE 110 can have inputs fromboth a DC control unit 140 and an automatic gain control (AGC) unit 150,and the AFE 110 can include a variable-gain amplifier (VGA), which canbe regulated by the AGC 150.

The AFE 110 includes an asymmetry correction circuit (ASC) 112configured to receive the analog readback signal and to compensate forasymmetry in the analog readback signal based on a coefficientadjustment received from a control circuit 130, such as a least meansquared (LMS) control circuit described below. The AFE 110 can alsoinclude a differentiator and a continuous time filter (CTF) 114.

The storage system can employ perpendicular magnetic recording (PMR)techniques, and a differentiator can be used in the AFE 110 todifferentiate the readback signal to make the signal look like that froma longitudinal magnetic recording (LMR) channel (the first derivative ofa PMR readback waveform can correspond to what an LMR readback waveformwould look like for the same data pattern). Thus, the remainder of theread channel can then be designed just as done for LMR. Thedifferentiator can be a bypassable differentiating circuit, which can beeither a separate component in the AFE 110 or integrated into anothercomponent of the AFE 110. For example, the differentiator can beintegrated into the CTF 114, which can have a program parameter thatallows differentiation to be turned on and off. Also, when reading PMRusing differentiation, a direct current (DC) free target should be used(as discussed further below) because the differentiation removes the DCcomponents in the signal.

An analog to digital converter (ADC) 115 converts the readback signalfrom continuous-time domain to discrete-time domain, and a signalequalizer 120 shapes the signal to a desired target response. The ADC115 can be a 6-bit ADC. The signal equalizer 120 can be a finite impulseresponse (FIR) digital filter, such as a 9-tap or 10-tap FIR, which canbe programmable or adaptive. For example, the system can include anadaptation unit 125 that provides a control input to the signalequalizer 120. Moreover, a CTF, ADC and FIR taken together can be viewedas the signal equalizer within the read channel; in general, the mainfunction of the CTF is noise filtering (e.g., filtering out the unwantedout-of-band noise), but the CTF can also provide some equalization.

A discrete time sequence detector 135 examines and interprets its inputas discrete values stored on the media 100. Timing control circuitry,including a timing control unit 160, a phase locked loop (PLL), or both,can be used to regulate the filtered signal provided to the detector135, and the DC control unit 140 can also apply a DC correction at oneor more locations in the main read path. The sequence detector 135 caninclude one or more components, such as a Viterbi detector. The mainread path can combine partial-response equalization withmaximum-likelihood sequence detection (PRML) using a discrete-timeapproach (e.g., the class-IV partial response target (PR-IV)).

An output of the sequence detector 135 can be provided to a postprocessor, such as a media noise processor (MNP) that identifies andcorrects errors in a detected sequence. As will be appreciated, multiplecomponents can be included after the component that obtains the binarysequence from the output of the signal equalizer, and these multiplecomponents can be separate electronic components or integrated into asingle sequence detector 135. For example, a single Viterbi detectorcomponent in a read channel can be used to obtain the binary sequenceand also to reconstruct the ideal target channel output as describedfurther below, or a Viterbi detector component can be used to obtain thebinary sequence and another component (e.g., MNP), which is responsiveto an output of the Viterbi detector component, can be used toreconstruct the ideal target channel output.

In general, multiple output values of the sequence detector 135, such asoutput values coming directly from the sequence detector 135 or from apost processor, is provided to a control circuit 130. The controlcircuit 130 provides the coefficient adjustment to the ASC 112 to affectthe asymmetry compensation based on an estimate of nonlinearity derivedfrom the equalized signal and the multiple output values of the discretetime sequence detector.

FIG. 2 is a block diagram illustrating the introduction of nonlinearityin the readback signal and the subsequent compensation for thisnonlinearity. H(jω) 200 represents the transfer characteristics of thehead-media combination, absent asymmetry. An asymmetry component 205represents the asymmetry introduced by the head when reading the media.This asymmetry adds nonlinear component(s) to the signal and can thus berepresented by the following polynomial: x+p₂·x²+p₃·x³+p₄·x⁴+ . . . ,where x is the readback signal, and p₂, p₃, p₄, . . . are the amounts ofhigher order nonlinearity added to the signal. Typically, the secondorder term of the asymmetry polynomial is the most significant highorder term. Various portions of the description below addressesasymmetry correction using only the linear term and the second orderterm, but the systems and techniques described are also applicable tohigher order asymmetry corrections.

Noise 210 is added (this can be electronic noise in the channel and canalso partially come from the head-media combination). An ASC 215compensates for the asymmetry by applying an asymmetry correction basedon a model of the asymmetry in the channel. This asymmetry correctioncan be represented by the following polynomial: x−q₂·x²−q₃·x³−q₄·x⁴ . .. . The asymmetry correction employed by the ASC 215 can be limited tothe second order (x−q·x²) or additional higher order terms can beincluded in the asymmetry correction. In general, one or morecoefficients, q₂, q₃, q₄, . . . , are adjusted so as to cancel thecorresponding nonlinear elements in the readback signal. Thenonlinearity introduced by the ASC 215 thus counteracts the nonlinearityintroduced into the readback signal by the head-media combination,before passing the readback signal on to a CTF 220 (which can include aprogrammable differentiator 222) and an ADC 225.

The one or more coefficients can be decided adaptively, on the fly, tocounteract nonlinearity in the readback signal as it is observed. An LMScontrol circuit 245 can actively adjust the one or more coefficientsused by the ASC 215 based on an estimate of nonlinearity derived fromthe output of an FIR 230 and multiple output values from a postprocessor 240. The FIR output provides a signal that reflects thenonlinearity in the channel, and a Viterbi detector 235 providespreliminary decision bits to the post processor 240, which reconstructsthe ideal target channel output used to calculate the error signal inthe LMS control circuit 245. Moreover, the Viterbi detector 235 and thepost processor 240 can be integrated into a single detector thatreconstructs the ideal channel output.

The read channel can be used in both LMR and PMR applications, and theread channel can be used with various target polynomials (which may beselected as desired for the specific application). In the case of PMRwith differentiation, as described above, the read signal can beconverted into a form that looks like that seen in LMR, and a largeportion of the read channel can be designed in the manner appropriatefor LMR. In this case, the target polynomial can be a DC-free target.

A typical DC-free target is [5, 3, −3, −3, −2]. Since asymmetrycorrection is the signal aspect being addressed here, the rest of thechannel can be assumed to be ideal (e.g., any additive white noise canbe disregarded because it does not affect the asymmetry processing beingdescribed), and the FIR equalizer can be assumed to be doing a perfectjob in equalizing the signal to the target. The signal asymmetry isreflected at the FIR output, and thus the FIR output indicates theasymmetry in the signal. The FIR output can be used to decide howadjustments to the asymmetry correction should be made to cancel thatasymmetry. Processing the equalized signal in the discrete time domainallows generation of one or more indicators of the asymmetry, which canbe used to better correct for the asymmetry in the continuous timedomain.

The asymmetry in the signal passes through the CTF, ADC and FIR. Thus,the effect of the asymmetry is spread out in time during processing ofthe signal. Once the signal reaches the FIR 230, the prior applicationof the asymmetry 205 is in some sense spread out into a period of timeinstead of appearing at only one point in time. To model this type ofnonlinearity, a matrix model can be used. Using a sufficiently largeenough matrix, the effect of the spreading of the nonlinearity in thechannel can be modeled very accurately.

For example, the asymmetry can be modeled by a quadratic form equationas follows:y _(k) ^(a) ={right arrow over (B)} _(k) ^(T) ·Γ′+{right arrow over (B)}_(k) ^(t) ·Λ′·{right arrow over (B)} _(k) =Ŷ _(k) ^(T) ·Γ+Ŷ _(k) ^(T)·Λ·Ŷ _(k)  (1)where {right arrow over (B)}_(k) is a vector of the binary input bits,Ŷ_(k) is a vector of the ideal FIR output samples, and superscript Tindicates the vector is transposed; Γ′ and Γ are both one-columnmatrices characterizing the linear part of the signal; and Λ are bothsquare matrices characterizing the nonlinear part of the signal.

The first term, {right arrow over (B)}_(k) ^(T)·Γ′, is the linear termthat characterizes the linear relationship between the FIR output andthe binary input. The second term, {right arrow over (b)}_(k)^(T)·Λ′·{right arrow over (B)}_(k), is a quadratic form, so there aretwo vectors of binary input on both sides of a square matrix. Thus, thisequation gives the modeled relationship between the FIR output and thebinary input to the head-media channel.

In addition, the second part of the equation gives the modeledrelationship between the FIR output and the ideal FIR output, which isreadily available in the channel. The quadratic form equation models therelationship between the true FIR output and the ideal FIR output. Ŷ_(k)is a vector of ideal FIR output. Expanding this vector to clarify thenotation:

$\begin{matrix}{{\hat{Y}}_{k} = {\begin{matrix}y_{k - N}^{d} \\\vdots \\y_{k}^{d} \\\vdots \\y_{k + N}^{d}\end{matrix}}} & (2)\end{matrix}$Ŷ_(k) is a vector of the ideal FIR output for a period of time. Thisvector can be centered around the current time, which is k, and can goin both directions in time, including both the future ideal FIR outputvalues and the past ideal FIR output values. Here, the superscript “d”indicates that this is the ideal FIR output (the reconstructed FIRoutput, which is the signal after some signal processing andreconstruction).

A Minimum Mean Square Error (MMSE) criterion can be used to decide thematrices in the above modeling. Simulations of this modeling indicatehigh accuracy. For example, with a DC-free target of [5, 3, −3, −3, −2],30% asymmetry, 1×25 and 25×25 modeling matrices, the simulatedidentification error, defined as the difference between the real FIRoutput Y_(r)(k) and the identified FIR output Y_(a)(k), is shown in agraph 300 in FIG. 3. As shown, the error can be very small once theconverged values of the F and A matrices are obtained, and thenonlinearity is accurately summarized by the second term of equation(1), Ŷ_(k) ^(T)·Λ·Ŷ_(k), which is governed by the Λ matrix. Most of theinformation regarding the MR asymmetry will typically be provided by theΛ matrix.

The asymmetry nonlinearity is modeled in a 25×25 matrix. To do asymmetrycorrection, a subset of the six hundred and twenty five (25 times 25)matrix elements can be used as indicators of the amount and direction ofMR asymmetry identified in the matrix. Moreover, a set of suchindicators can be selected for use with multiple target polynomials byexamining the matrices in some specific cases.

Table 1 shows a portion of a converged, asymmetry matrix generated for atarget of [5, 3, −3, −3, −2], with 30% asymmetry; the portion shown isthe core 13×13 matrix of the nonlinear modeling (the most significantinformation is found in the center of the 25×25 matrix, thus only thecore 13×13 matrix within the 25×25 matrix is shown here):

TABLE 1 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 k − 6 k − 5 k − 4 k −3 k − 2 k − 1 k k + 1 k + 2 k + 3 k + 4 k + 5 k + 6 R1 0.06 0.03 −0.140.04 0.08 −0.27 −0.13 0.03 −0.02 0.01 −0.03 0.01 −0.04 k − 6 R2 0.03−0.22 0.30 −0.17 −0.06 0.27 −0.38 −0.04 0.02 0.06 0.02 −0.01 0.01 k − 5R3 −0.14 0.30 −0.31 0.36 0.10 −0.51 0.02 −0.18 0.15 −0.19 0.09 −0.110.06 k − 4 R4 0.04 −0.17 0.36 −0.51 0.01 0.32 −0.72 −0.11 −0.04 0.11−0.02 0.08 −0.05 k − 3 R5 0.08 −0.06 0.10 0.01 0.07 −0.38 0.05 0.33−0.18 0.10 −0.16 0.07 −0.10 k − 2 R6 −0.27 0.27 −0.51 0.32 −0.38 0.36−0.48 −0.64 0.60 −0.31 0.40 −0.23 0.28 k − 1 R7 −0.13 −0.38 0.02 −0.720.05 −0.48 −0.32 0.44 −0.06 0.47 0.09 0.39 0.09 k R8 0.03 −0.04 −0.18−0.11 0.33 −0.64 0.44 0.54 0.10 0.33 −0.06 0.19 −0.09 k + 1 R9 −0.020.02 0.15 −0.04 −0.18 0.60 −0.06 0.10 0.21 −0.23 0.07 −0.15 0.04 k + 2R10 0.01 0.06 −0.19 0.11 0.10 −0.31 0.47 0.33 −0.23 −0.02 0.01 0.06 0.01k + 3 R11 −0.03 0.02 0.09 −0.02 −0.16 0.40 0.09 −0.06 0.07 0.01 0.11−0.11 0.01 k + 4 R12 0.01 −0.01 −0.11 0.08 0.07 −0.23 0.39 0.19 −0.150.06 −0.11 0.03 −0.02 k + 5 R13 −0.04 0.01 0.06 −0.05 −0.10 0.28 0.09−0.09 0.04 0.01 0.01 −0.02 0.06 k + 6

The elements of this matrix reflect the nonlinearity of the signal. Mostof the elements are very close to zero. However, many of the elementsnear the center of the matrix and around the main diagonal have largevalues and can be good indicators of nonlinearity in the signal and alsoof the direction of that nonlinearity. By looking at multiple matricesgenerated for different targets, a set of matrix elements can beselected and used as good indicators of asymmetry in the signal. Thetarget polynomial selected for a given channel is generally independentof asymmetry in that channel and is mostly a function of the channeldensity and signal to noise ratio. Using the systems and techniquesdescribed, a read channel transceiver device can be designed for usewith multiple different target polynomials and in multiple differentapplications.

Table 2 shows the core portion (the core 13×13 matrix of the nonlinearmodeling) of a converged, asymmetry matrix generated for a target of [4,3, −2, −3, −2], with 30% asymmetry:

TABLE 3 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 k − 6 k − 5 k − 4 k −3 k − 2 k − 1 k k + 1 k + 2 k + 3 k + 4 k + 5 k + 6 R1 0.08 0.05 −0.07−0.03 0.10 −0.19 −0.32 −0.03 0.06 −0.02 −0.02 0.02 −0.01 k − 6 R2 0.05−0.16 0.24 −0.05 −0.05 0.14 −0.29 −0.06 −0.02 0.06 0.02 −0.00 0.01 k − 5R3 −0.07 0.24 −0.28 0.30 0.15 −0.34 −0.15 −0.17 0.21 −0.17 0.04 −0.060.01 k − 4 R4 −0.03 −0.05 0.30 −0.41 −0.05 0.11 −0.67 −0.28 −0.03 0.080.01 0.05 0.01 k − 3 R5 0.10 −0.05 0.15 −0.05 0.09 −0.35 −0.17 0.36−0.14 0.02 −0.16 0.03 −0.11 k − 2 R6 −0.19 0.14 −0.34 0.11 −0.35 0.39−0.36 −0.55 0.49 −0.12 0.28 −0.07 0.19 k − 1 R7 −0.32 −0.29 −0.15 −0.67−0.17 −0.36 −0.38 0.29 0.24 0.38 0.26 0.35 0.27 k R8 −0.03 −0.06 −0.17−0.28 0.36 −0.55 0.29 0.62 0.06 0.30 −0.03 0.20 −0.06 k + 1 R9 0.06−0.02 0.21 −0.03 −0.14 0.49 0.24 0.06 0.18 −0.09 −0.09 −0.10 −0.04 k + 2R10 −0.02 0.06 −0.17 0.08 0.02 −0.12 0.38 0.30 −0.09 −0.14 0.03 0.030.02 k + 3 R11 −0.02 0.02 0.04 0.01 −0.16 0.28 0.26 −0.03 −0.09 0.030.10 −0.11 0.00 k + 4 R12 0.02 −0.00 −0.06 0.05 0.03 −0.07 0.35 0.20−0.10 0.03 −0.11 −0.05 0.00 k + 5 R13 −0.01 0.01 0.01 0.01 −0.11 0.190.27 −0.06 −0.04 0.02 0.00 0.00 0.01 k + 6

Table 3 shows the core portion (the core 13×13 matrix of the nonlinearmodeling) of a converged, asymmetry matrix generated for a target of [7,4, −4, −5, −2], with 30% asymmetry:

TABLE 3 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 k − 6 k − 5 k − 4 k −3 k − 2 k − 1 k k + 1 k + 2 k + 3 k + 4 k + 5 k + 6 R1 0.22 −0.01 −0.370.51 −0.08 −0.30 0.05 0.03 −0.02 −0.02 0.03 −0.03 −0.01 k − 6 R2 −0.01−0.41 0.86 −1.03 0.20 0.29 −0.28 −0.17 0.04 0.04 0.01 0.01 0.01 k − 5 R3−0.37 0.86 −1.43 1.46 −0.46 −0.69 0.28 0.13 −0.07 −0.04 0.02 −0.02 −0.02k − 4 R4 0.51 −1.03 1.46 −1.32 0.24 0.95 −0.90 −0.39 0.11 −0.01 0.02−0.00 0.03 k − 3 R5 −0.08 0.20 −0.46 0.24 0.48 −1.59 1.11 0.41 −0.200.03 0.00 0.02 0.00 k − 2 R6 −0.30 0.29 −0.69 0.95 −1.59 1.75 −1.39−0.46 0.39 0.07 0.13 0.02 0.10 k − 1 R7 0.05 −0.28 0.28 −0.90 1.11 −1.390.76 0.45 −0.24 0.02 0.04 0.09 0.06 k R8 0.03 −0.17 0.13 −0.39 0.41−0.46 0.45 −0.18 0.44 0.29 0.15 0.07 0.08 k + 1 R9 −0.02 0.04 −0.07 0.11−0.20 0.39 −0.24 0.44 −0.05 −0.18 −0.04 −0.04 −0.01 k + 2 R10 −0.02 0.04−0.04 −0.01 0.03 0.07 0.02 0.29 −0.18 0.07 0.06 0.04 0.03 k + 3 R11 0.030.01 0.02 0.02 0.00 0.13 0.04 0.15 −0.04 0.06 0.04 −0.06 −0.03 k + 4 R12−0.03 0.01 −0.02 −0.00 0.02 0.02 0.09 0.07 −0.04 0.04 −0.06 −0.02 0.01k + 5 R13 −0.01 0.01 −0.02 0.03 0.00 0.10 0.06 0.08 −0.01 0.03 −0.030.01 0.04 k + 6

The matrices given in Tables 1, 2 and 3 are symmetrical about the maindiagonal [(R1,C1), (R2,C2), . . . , (R12,C12), (R13,C13)]. The centerelement in each matrix (R7,C7), which is at the intersection of the 7thcolumn (C7) and 7th row (R7), corresponds to the current time index “k”.Each element in these matrices represents the relationship between thereal FIR output and a certain product of the ideal FIR output.

The center element (R7,C7) corresponds to the square of the current FIRoutput (y_(k) ^(d)·y_(k) ^(d)). The remaining elements on the maindiagonal correspond to the squares of the past and future FIR outputs(y_(k−6) ^(d)·y_(k−6) ^(d), . . . , y_(k−1) ^(d)·y_(k−1) ^(d), y_(k+1)^(d)·y_(k+1) ^(d), . . . , y_(k+6) ^(d)·y_(k+6) ^(d)). The elements offthe main diagonal correspond to products of the FIR output at differentdiscrete times (product terms having different time index subscripts).Thus, the element (R8,C7) corresponds to the product y_(k) ^(d)·y_(k+1)^(d).

By examining multiple matrices, such as above, matrix elements that aresignificant in the nonlinear modeling in each of the multiple matricescan be identified. For example, in the three cases shown above, theshaded matrix elements can be selected for use in controlling asymmetrycorrection in the channel:

TABLE 4 Matrix Elements Nonlinear ModelingTerms element (R3, C6) →y_(k−1) ^(d) · y_(k−4) ^(d) element (R4, C7) → y_(k) ^(d) · y_(k−3) ^(d)element (R5, C6) → y_(k−1) ^(d) · y_(k−2) ^(d) element (R6, C7) → y_(k)^(d) · y_(k−1) ^(d) element (R7, C8) → y_(k+1) ^(d) · y_(k) ^(d) element(R6, C8) → y_(k−1) ^(d) · y_(k+1) ^(d) element (R5, C8) → y_(k+1) ^(d) ·y_(k−2) ^(d) element (R6, C9) → y_(k+2) ^(d) · y_(k−1) ^(d)Table 4 shows example matrix elements, and their corresponding nonlinearmodeling terms (from equations (1) and (2) above), which are useful incontrolling asymmetry correction.

In addition, such matrix elements flip their signs when the asymmetry isswitched to an opposite polarity. Thus, the nonlinear modeling termsobtained using this matrix approach can be used as indicators of thepresence of asymmetry and its polarity. When asymmetry correction isapplied, such individual terms or their combination can be used as aguideline to show if the current asymmetry correction is adequate, inwhich direction the correction should be adjusted, or both.

FIG. 4 is a flowchart illustrating a process of selecting signalindicators of asymmetry for use in asymmetry correction. Multipleasymmetry matrices that model asymmetry in a received analog signal,including an effect of asymmetry spreading in a read channel, aregenerated at 410. This can involve generating asymmetry matrices thatcharacterize relationships between true FIR output and reconstructed,ideal FIR output for different targets, including a DC target and aDC-free target, as described further below.

The multiple asymmetry matrices are compared at 420. This can involvedetermining one or more matrix elements that have significantcorrelation with the asymmetry across the multiple matrices, where theone or more matrix elements are off a main matrix diagonal. The criteriaused in choosing the indicators can have three main aspects: (1) theindicator should have consistent signs in the sense that the indicator,as defined by an element at a particular position in the matrix, doesnot change sign across different matrices generated by different targetchannels as long as the polarity of the asymmetry applied is not alsochanged; (2) the values of the indicators should be significant comparedto the remaining matrix elements (e.g., the value of an indicator shouldbe no less than 10% of the maximum element values of the matrixregardless of the target channels); and (3) the value of an indicatorshould be, in general, linearly proportional to the amount of asymmetryapplied prior to any asymmetry correction.

Indicators of asymmetry are selected from the matrices based on thecomparison at 430. This can involve deciding which indicators to includein a read channel device being designed, or this can involve assigningrelative contributions of the indicators for use in asymmetry correctionin a read channel device that has been designed to include multipleprogrammable asymmetry indicators in accordance with the presentspecification.

Thus, in general, one or more asymmetry indicators can be derived byfinding common indicators of nonlinearity in a signal across differenttarget polynomials. A single such indicator may be used to controlasymmetry correction or multiple such indicators may be used. Inaddition, many indicators may be selected for use in a device (e.g., aread channel transceiver device), and the device can include programfunctionality allowing reduction of the influence of one or more of theselected indicators (including potentially turning off one or more ofthe indicators). Thus, the indicators used in a given application can beprogrammed as desired.

For example, two indicators can be used as a reliable indication ofasymmetry and the remaining indicators can be ignored. Thus, thenonlinear identification can be modeled by the following asymmetrypolynomial:y _(k) ^(a) =α·y _(k) ^(d) +β·y _(k) ^(d)·(y _(k+1) ^(d) −y _(k)^(d−1))  (3)where y^(d) is the ideal channel output, y^(a) is the real outputaccording to the asymmetry model, α models the gain factor of theequalized channel, and β indicates the presence of asymmetry. Using thismodel, the coefficients of the asymmetry polynomial (α and β) can bedetermined and used to adjust the asymmetry correction.

The coefficients α and β can be adaptively decided using the LMS controlcircuit 245. An error signal is defined according to the followingequation:e _(k) =y _(k) ^(r) −y _(k) ^(a)  (4)where y^(r) is the real FIR output with MR asymmetry included and y^(a)is the modeled/identified FIR output with the nonlinearity taken intoaccount in the modeling, from equation (3). The model of nonlinearity inthe readback signal can thus be made more accurate by making y^(a) asclose to y^(r) as possible. With this error signal defined, thecoefficients of the nonlinearity model (and consequently thecoefficients used by the ASC) can be adjusted using least mean squarederror criteria based on the products corresponding to the selectedmatrix indicators.

Thus, α and β can be determined by the following equations:α_(k+1)=α_(k)+μ_(a) ·e _(k) ·y _(k) ^(d)  (5)β_(k+1)=β_(k)+μ_(b) ·e _(k) ·y _(k) ^(d)·(y _(k+1) ^(d) −y _(k−1)^(d))  (6)using the LMS control circuit 245. Once the values of α and β arereliably determined, the adaptation of the asymmetry correctioncoefficient can be given by:q _(k+1) =q _(k)+μ·β  (7)where q is the asymmetry correction coefficient, and μ is a step size inthe adjustment of the coefficient. As β goes to zero, the asymmetry isthereby reduced or removed. Note that μ may be a programmable parameterin a system, as described further below, or μ may be an implicitparameter and not expressly defined.

The example matrices shown above are for the case of using a DC-freetarget with a possible differentiator used with the CTF. In practice, aDC target can also be used. In the case of a DC target, thecharacteristics of the matrices modeling the asymmetry will bedifferent. An example is shown in Table 5.

Table 5 shows the core portion (the core 13×13 matrix of the nonlinearmodeling) of a converged, asymmetry matrix generated for a DC target of[5, 6, 0, −1], with 30% asymmetry:

TABLE 5 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 k − 6 k − 5 k − 4 k −3 k − 2 k − 1 k k + 1 k + 2 k + 3 k + 4 k + 5 k + 6 R1 0.01 0.00 0.010.01 −0.00 −0.01 0.02 0.03 0.00 −0.00 −0.00 0.00 −0.01 k − 6 R2 0.00−0.01 −0.01 −0.03 0.01 0.01 −0.03 −0.03 −0.01 0.00 −0.00 0.00 0.00 k − 5R3 0.01 −0.01 0.04 0.00 0.06 0.02 −0.01 0.02 −0.00 0.00 −0.00 −0.00−0.00 k − 4 R4 0.01 −0.03 0.00 −0.12 0.04 0.03 −0.08 −0.04 −0.00 −0.00−0.01 0.01 −0.00 k − 3 R5 −0.00 0.01 0.06 0.04 0.38 0.11 −0.20 −0.06−0.01 0.01 −0.00 −0.00 −0.00 k − 2 R6 −0.01 0.01 0.02 0.03 0.11 −0.10−0.43 −0.13 0.02 −0.03 0.02 −0.02 0.02 k − 1 R7 0.02 −0.03 −0.01 −0.08−0.20 −0.43 −1.20 −0.46 0.03 −0.06 0.04 −0.04 0.03 k R8 0.03 −0.03 0.02−0.04 −0.06 −0.13 −0.46 0.07 0.13 −0.01 0.02 −0.01 0.01 k + 1 R9 0.00−0.01 −0.00 −0.00 −0.01 0.02 0.03 0.13 0.15 0.01 −0.01 0.01 −0.01 k + 2R10 −0.00 0.00 0.00 −0.00 0.01 −0.03 −0.06 −0.01 0.01 −0.10 −0.01 0.01−0.01 k + 3 R11 −0.00 −0.00 −0.00 −0.01 −0.00 0.02 0.04 0.02 −0.01 −0.010.06 0.01 −0.00 k + 4 R12 0.00 0.00 −0.00 0.01 −0.00 −0.02 −0.04 −0.010.01 0.01 0.01 −0.04 −0.00 k + 5 R13 −0.01 0.00 −0.00 −0.00 −0.00 0.020.03 0.01 −0.01 −0.01 −0.00 −0.00 0.02 k + 6

In this matrix, the most significant term is the center element (R7,C7).In comparison, the other elements are relatively small. Thus, in thecase of DC targets, the squared ideal equalized output value for thecurrent time should usually be included in the nonlinear modeling. Thus,this matrix element can be included in the modeling, such as in thefollowing example equations:y _(k) ^(a) =α·y _(k) ^(d) +β·y _(k) ^(d)·(y _(k+1) ^(d) −y _(k−1)^(d))+χ·y _(k) ^(d) ·y _(k) ^(d)  (8)χ_(k+1)=χ_(k)+μ_(c) ·e _(k) ·y _(k) ^(d) ·y _(k) ^(d)  (9)χ indicates the presence of asymmetry based on the squared term of thematrix center and can be adaptively decided using the LMS controlcircuit 245. Adaptation of an asymmetry correction coefficient can alsobe influenced by this squared term, such as in:q _(k+1) =q _(k)μ·(β−χ)  (10)Alternatively, χ and β can be split up and used with programmable stepsizes, as in:q _(k+1) =q _(k)+μ₁β−μ₂χ  (11)The programmable values μ₁ and μ₂ provide programmable control over theinfluence of various asymmetry indicators in the asymmetry correction,including potentially turning off an indicator all together. Forexample, as shown in FIG. 2, the LMS control circuit 245 can include aprogramming interface 247 with inputs for μ₁ and μ₂ that enable programcontrol over relative contributions of the asymmetry indicators, (y_(k)^(d)·y_(k+1) ^(d)−y_(k) ^(d)·y_(k−1) ^(d)) and (y_(k) ^(d)·y_(k) ^(d)).

Moreover, multiple programmable values (μ₁ . . . μ_(N)) can be used withmultiple asymmetry indicators, which can be grouped in various ways. Inthe example above, indicators (R6,C7) and (R7,C8) are grouped with β andthe indicator (R7,C7) stands alone with χ. However, more or fewerindicators can be used, and these indicators can be grouped in variousways to provide program control over the asymmetry correction.

This technique can determine the nonlinearity at the FIR output and canbe directly applied to the adjustment of the coefficients in the ASC.The asymmetry correction can be applied in the analog, continuous timedomain (e.g., as close to the asymmetry component 205 as possible).

FIG. 5 is a block diagram illustrating an example ASC 500. The ASC 500is implemented in an analog circuit in the continuous time domain. TheASC 500 adjusts the readback signal 505 by feeding it through a squaringcircuit 510 and a multiplier circuit 530 to obtain an adjusted signalthat is then added back into the readback signal 505. The squaringcircuit 510 squares the signal 505, the multiplier circuit 530 mixes thesquared signal with a second order coefficient value 520, and the resultis combined with the readback signal 505 in an adder circuit 540.Additional higher order adjustments can also be built into the ASC 500.

The signal processor components described can be implemented as one ormore devices, such as one or more integrated circuit (IC) devices, in astorage device. FIG. 6 is a block diagram showing a magnetic-media diskdrive that employs amplitude asymmetry correction as described. The diskdrive includes a head-disk assembly (HDA) 600 and drive electronics 650(e.g., a printed circuit board assembly (PCBA) with semiconductordevices). The HDA 600 includes one or more disks 610 mounted on anintegrated spindle and motor assembly 615. The spindle and motorassembly 615 rotates the disk(s) 610 under read-write head(s) connectedwith a head assembly 620 in the HDA 600. The disk(s) 610 can be coatedwith a magnetically hard material (e.g., a particulate surface or athin-film surface) and can be written to, or read from, a single side orboth sides of each disk.

A head 632 on an arm 630 can be positioned as needed to read data on thedisk. A motor, such as a voice coil motor, can be used to position thehead over a desired track. The arm 630 can be a pivoting or sliding armand can be spring-loaded to maintain a proper flying height for the head632 in any drive orientation. A closed-loop head positioning system canbe used.

The HDA 600 can include a preamp/writer 640, where head selection andsense current value(s) can be set. The preamp/writer 640 can amplify areadback signal before outputting it to signal processing circuitry 670.The signal processing circuitry 670 can include a readback signalcircuit, a servo signal processing circuit, and a write signal circuit.

Signals between the HDA 600 and the drive electronics 650 can be carriedthrough a flexible printed cable. A controller 680 can direct a servocontroller 660 to control mechanical operations, such as headpositioning through the head assembly 620 and rotational speed controlthrough the motor assembly 615. The controller 680 can be one or more ICchips (e.g., a combo chip), which can include read/write channel signalprocessing circuitry 670. The controller 680 can be a microprocessor anda hard disk controller. The drive electronics 650 can also includevarious interfaces, such as a host-bus interface, and memory devices,such as a read only memory (ROM) for use by a microprocessor, and arandom access memory (RAM) for use by a hard disk controller. Theread/write channel 670 can also include error correction circuitry(e.g., MNP).

The amplitude asymmetry correction circuitry can be integrated with oneor more of the components described above or organized into a separatecomponent of a disk drive. For example, the amplitude asymmetrycorrection circuitry can be integrated into the controllers 660, 680,the read/write channel 670, the preamp/writer 640, or variouscombinations of these components (e.g., the components 660, 670, 680 canall be combined into a single integrated circuit). Moreover, theamplitude asymmetry correction circuitry can be integrated into adevice, such as a read/write channel transceiver device (e.g., theread/write channel 670), suitable for use in a magnetic recordingsystem; and this device can be configured to be usable with bothlongitudinal magnetic recording (LMR) and perpendicular magneticrecording (PMR).

FIG. 7 is a block diagram showing PMR as can be used in themagnetic-media disk drive of FIG. 6. A read-write head 700 flies over aPMR storage disk 710. The head 700 records bits perpendicular to theplane of the disk. The PMR disk 710 includes a high permeability(“soft”) magnetic under-layer 720 between a perpendicularly magnetizedthin film data storage layer 730 and the substrate 740. An image of themagnetic head pole created by the head 700 is produced in themagnetically soft under-layer 720. Consequently, the storage layer 730is effectively in the gap of the recording head, where the magneticrecording field is larger than the fringing field produced by a LMRhead. A read/write channel transceiver device designed for use with bothPMR and LMR can include a differentiator to take the first derivative ofthe readback signal in the case PMR, as described above.

FIG. 8 is a flowchart illustrating a process of asymmetry correction ascan be performed in a storage system. An analog signal is received froma storage medium at 810. Asymmetry in the analog signal is compensatingfor based on at least one coefficient adjustment at 820.

A digital signal obtained by sampling the analog signal is equalized at830. A data sequence is detected in the digital signal at 840. An idealtarget channel output is reconstructed from the detected data sequenceat 850. The coefficient adjustment is modified to affect the asymmetrycompensation based on an estimate of nonlinearity derived from thedigital equalized signal and reconstructed ideal target channel outputvalues corresponding to different discrete times at 860.

The processes described above, and all of the functional operationsdescribed in this specification, can be implemented in electroniccircuitry, computer hardware, firmware, software, or in combinations ofthem, such as the structural means disclosed in this specification andstructural equivalents thereof, including a software program operable tocause one or more machines to perform the operations described. It willbe appreciated that the order of operations presented is shown only forthe purpose of clarity in this description. No particular order may berequired for these operations, and various operations can occursimultaneously.

A few embodiments have been described in detail above, and variousmodifications are possible. Thus, other embodiments may be within thescope of the following claims.

What is claimed is:
 1. A method comprising: generating asymmetry vectorsthat model asymmetry in a received analog signal, including an effect ofasymmetry spreading in a read channel; selecting at least two differentindicators of asymmetry based on comparing one or more characteristicsof the asymmetry vectors; and using the selected indicators of asymmetryto compensate for one or more asymmetries associated with the analogsignal.
 2. The method of claim 1, wherein the generating comprisesgenerating asymmetry vectors that characterize relationships betweentrue finite impulse response (FIR) output and reconstructed, ideal FIRoutput for different targets, including a DC target and a DC-freetarget.
 3. The method of claim 1, wherein the generating comprisesgenerating the asymmetry vectors for different targets for modelingsignal nonlinearity caused by a magnetic recording channel asymmetryassociated with the read channel.
 4. The method of claim 1, comprising:determining, based on one or more of the asymmetry vectors, one or morevector elements having significant correlation with an asymmetryindicated by the multiple asymmetry vectors, wherein the selectingcomprises using the one or more determined vector elements.
 5. Themethod of claim 1, wherein the selecting comprises assigning relativecontributions of the indicators for use in asymmetry correction.
 6. Themethod of claim 1, wherein the selecting comprises selecting anindicator whose sign is identical in all of the asymmetry vectors. 7.The method of claim 1, wherein the selecting comprises selecting largestvalued elements of the asymmetry vectors.
 8. A non-transitory storagemedium encoded with a software program operable to cause one or moremachines to perform operations comprising: generating asymmetry vectorsthat model asymmetry in a received analog signal, including an effect ofasymmetry spreading in a read channel; selecting at least two differentindicators of asymmetry based on comparing one or more characteristicsof the asymmetry vectors; and using the selected indicators of asymmetryto compensate for one or more asymmetries associated with the analogsignal.
 9. The storage medium of claim 8, wherein the generatingcomprises generating asymmetry vectors that characterize relationshipsbetween true finite impulse response (FIR) output and reconstructed,ideal FIR output for different targets, including a DC target and aDC-free target.
 10. The storage medium of claim 8, wherein thegenerating comprises generating asymmetry vectors for different targetsfor modeling signal nonlinearity caused by a magnetic recording channelasymmetry associated with the read channel.
 11. The storage medium ofclaim 8, wherein the operations comprise: determining, based on one ormore of the asymmetry vectors, one or more vector elements havingsignificant correlation with an asymmetry indicated by the multipleasymmetry vectors, wherein the selecting comprises using the one or moredetermined vector elements.
 12. The storage medium of claim 8, whereinthe selecting comprises assigning relative contributions of theindicators for use in asymmetry correction.
 13. The storage medium ofclaim 8, wherein the selecting comprises selecting an indicator whosesign is identical in all of the vectors.
 14. The storage medium of claim8, wherein the selecting comprises selecting largest valued elements ofthe vectors.
 15. An apparatus comprising: circuitry to receive dataindicative of an analog signal; circuitry configured to generateasymmetry vectors that model asymmetry in the analog signal, includingan effect of asymmetry spreading in a read channel; circuitry configuredto select at least two different indicators of asymmetry based on theasymmetry vectors, and circuitry configured to (i) assign relativecontributions of the indicators for use in asymmetry correction, (ii)select an indicator whose sign is identical in all of the vectors, (iii)select largest valued elements of the vectors, (iv) or a combinationthereof.
 16. The apparatus of claim 15, wherein the circuitry configuredto generate the asymmetry vectors is configured to generate asymmetryvectors that characterize relationships between true finite impulseresponse (FIR) output and reconstructed, ideal FIR output for differenttargets, including a DC target and a DC-free target.
 17. The apparatusof claim 15, wherein the circuitry configured to generate the asymmetryvectors is configured to generate asymmetry vectors for differenttargets for modeling signal nonlinearity caused by a magnetic recordingchannel asymmetry associated with the read channel.
 18. The apparatus ofclaim 15, further comprising: circuitry configured to determine, basedon one or more of the asymmetry vectors, one or more vector elementshaving significant correlation with an asymmetry indicated by themultiple asymmetry vectors.
 19. The apparatus of claim 15, furthercomprising: circuitry configured to use the selected indicators ofasymmetry to compensate for one or more asymmetries associated with theanalog signal.
 20. A system, comprising: a read channel to produce ananalog signal; and circuitry configured to generate asymmetry vectorsthat model asymmetry in the analog signal, including an effect ofasymmetry spreading in the read channel, select at least two differentindicators of asymmetry based on comparing one or more characteristicsof the asymmetry vectors, and use the selected indicators of asymmetryto compensate for one or more asymmetries associated with the analogsignal.
 21. The system of claim 20, wherein comparing the one or morecharacteristics of the asymmetry vectors includes assigning relativecontributions of the indicators for use in asymmetry correction,identifying an indicator whose sign is identical in all of the asymmetryvectors, determining largest valued elements of the asymmetry vectors,or a combination thereof.
 22. The system of claim 20, wherein thecircuitry is configured to generate asymmetry vectors that characterizerelationships between true finite impulse response (FIR) output andreconstructed, ideal FIR output for different targets, including a DCtarget and a DC-free target.
 23. The system of claim 20, wherein thecircuitry is configured to generate asymmetry vectors for differenttargets for modeling signal nonlinearity caused by a magnetic recordingchannel asymmetry associated with the read channel.
 24. The system ofclaim 20, wherein the circuitry is configured to determine, based on oneor more of the asymmetry vectors, one or more vector elements havingsignificant correlation with an asymmetry indicated by the multipleasymmetry vectors.